CS W3134: Data Structures in Java

Transcription

1 CS W3134: Data Structures in Java Lecture #10: Stacks, queues, linked lists 10/7/04 Janak J Parekh HW#2 questions? Administrivia Finish queues Stack/queue example Agenda 1

2 Circular queue: miscellany Having to keep count is a little extra work Book has sample code to deal with no-count implementation, but more complex Basic problem: how to tell queue empty vs. full Trick: if full, leave an empty space We re not going to do this Other queues Deque: double-ended queue essentially a stack and queue combined: insert/remove left/right Priority queue Object of highest priority will be next to be dequeued After insert, front points to highest-priority element Book s s implementation does insertion sort: starts at end, and moves elements up until it s s in the right position No benefit to using circular constructs, so very similar to naïve queue approach Complexity? (Heaps are better, but later) More complex stack example How do computers parse arithmetic expressions? First step: transform expression into postfix notation Second step: evaluate postfix expression using a stack 2

3 Postfix Also called Reverse Polish Notation (RPN); HP calculators Why? Parentheses unneeded no ambiguity Can process in one pass from left-to to-right Fairly straightforward to translate from infix to postfix, but let s s hold off on this Evaluating a Postfix expression Go left-to to-right If operand, push on stack If operator, pop two operands, use operator, and push result on stack When done, there should be one value on the stack Pop it Converting Infix to Postfix See pages , 159, although I think these bullets make more sense ;) Need to encode operator precedence To process: Operand: write straight to output (: push on stack ): pop all items until ( encountered, and output them; don t write the ( Input complete: pop all items and write out Operator: interesting problem 3

4 Converting Infix-to to-postfix (II) Operator handling If stack is empty, push Else, pop, determine precedence of new vs. popped If popped is a (, put it back on the stack, and put the new operator on top Else if new has higher precedence, push popped back on, and push new on top of it Else if popped has higher or equal precedence, output it, and repeat this process (PE)MDAS for precedence Linked lists Arrays are rather limited, cumbersome data structures cells are fixed together, limited length What if we could break apart the cells? We can! In fact, linked list-style style structures are used more frequently unless you need very fast random index- based access Trees, graphs, etc. are generalizations of linked lists Linked List structure Two basic objects: The list parent itself An element (book calls link ), with data Technically, we don t t need both Parent contains reference to the first element Each element contains a reference to the next element Last element s next is set to null 4

5 Basic Linked List operations How to tell if empty? Insertions insertfirst() deletefirst() displaylist() insertlast() More complex operations How to find an arbitrary element? How to delete arbitrary element? Double-ended ended list Contains pointer to last element Makes insertlast() much faster (how much?) Linked list complexity? Similar to arrays O(1) insert/delete at beginning (or end of list for double-ended) ended) Other operations take O(N), but faster than array if sliding is needed in array Memory? Linked list more efficient, although it has to keep lots of references 5

6 Revisit abstraction Book finally covers abstraction here We can redo all of our previous data structures, previously array-backed backed,, as linked list-backed Interface high-level contract, while the dirty details are hidden How to do a stack? How to do a queue? You should read through this section Finish Linked Lists Start Recursion Next time 6